arXiv subjects

Guy Fabrice Foghem Gounoue

Publications and source records attributed to Guy Fabrice Foghem Gounoue.

3 recordsLinked to original sources

arXiv2024

$L^2$-Theory for nonlocal operators on domains

This thesis explores the $L^2$-Theory for nonlocal operators of Lévy type on bounded domains, as well as their local counterparts. The research was completed at Bielefeld University in Germany and has since garnered significant attention in the field of analysis of nonlocal operators. To enhance its visibility, we believe it is convenient to make it available on arXiv. Interested readers are strongly encouraged to use the following referencing format: "Guy Fabrice Foghem Gounoue. $L^2$-Theory for nonlocal operators on domains. PhD thesis, Bielefeld University, \url{https://doi.org/10.4119/unibi/2946033}, 2020."

math.AP↗

arXiv2023

A Remake of Bourgain-Brezis-Mironescu Characterization of Sobolev Spaces

We introduce a large class of concentrated $p$-Lévy integrable functions approximating the unity, which serves as the core tool from which we provide a nonlocal characterization of Sobolev spaces and the space of functions of bounded variation via nonlocal energies forms. It turns out that this nonlocal characterization is a necessary and sufficient criterion to define Sobolev spaces on domains satisfying the extension property. We also examine the general case where the extension property does not necessarily hold. In the latter case, we establish weak convergence of the nonlocal Radon measures involved to the local Radon measures induced by the distributional gradient.

math.AP↗

arXiv2019

Mosco convergence of nonlocal to local quadratic forms

We study sequences of nonlocal quadratic forms and function spaces that are related to Markov jump processes in bounded domains with a Lipschitz boundary. Our aim is to show the convergence of these forms to local quadratic forms of gradient type. Under suitable conditions we establish the convergence in the sense of Mosco. Our framework allows bounded and unbounded nonlocal operators to be studied at the same time. Moreover, we prove that smooth functions with compact support are dense in the nonlocal function spaces under consideration.

math.AP↗